A Bed is in the form of a circular sector of radius and central angle θ. Find its radius if the area of the sector is 100 cm2 and its perimeter is a minimum.

Answer 1

A = 1/2 r^2 θ = 100
The perimeter p is
p = 2r + rθ = r(θ+2) = r(200/r^2 + 2) = 200/r + 2r
dp/dr = 2 - 200/r^2 = 2/r^2 (r^2-100)
so p is a minimum when r = 10